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Vocabulary Review Unit Rates • A ratio is a comparison of two quantities by division. ̶ 17 out of 20 students, or 17 20 • A rate is a special type of ratio comparing two quantities with different units. – Driving 120 miles in 2 hours, or 120 miles 2 hours • A unit rate is a rate that is simplified so that it has a denominator of 1 unit. – Driving 120 miles in 2 hours, or 120 miles 60 miles 2 hours 1 hour Ratios • A ratio is a comparison of two numbers. o Example: Tamara has 2 dogs and 8 fish. The ratio of dogs to fish can be written in three different ways. Rate • What is a rate? – A rate is a ratio with 2 different units(measurement) • What is an example of a unit? – You ran 5 miles in 2 hours. A rate to represent you running would be 5 miles 2 hours – 5 apples cost $2.00. A rate to represent the cost of the apples would be $2.00 5 apples Unit Rate • What is a unit rate? – A unit rate is a rate with a denominator of 1. • Do unit rates of two different units? – YES, unit rates are rates and rates have two different units! • How do we find unit rate? – 1st: Set up a unit rate – 2nd: Divide by the denominator – 3rd: Write your answer in word form (the numerator PER the denominator). Example 1: Andy biked 24 miles in 4 hours. If he traveled at a constant speed, how many miles did he ride in 1 hour? Write a verbal model of what you are comparing. Substitute in the values given for each quantity. Since a unit rate has a denominator of 1 unit, divide the numerator and denominator by 4. miles hours 24 miles 4 hours 24 4 44 6 miles 1 hour Andy biked 6 miles per hour. Example 2: A 12-pack of Gatorade costs $13.44. What is the unit price per bottle? Write a verbal model of what you are comparing. Substitute in the values given for each quantity. Divide the numerator and denominator by 12 to find the unit rate. cost bottle $13.44 12 bottles $ 13 . 44 12 12 12 $1.12 1 bottle The unit price is $1.12 per bottle. Brianna posted a picture of her puppy on Instagram. When she checked her Phone 4 hours later she had 152 likes. How many likes did she get for her Picture per hour ? Blake posted a picure of his adorable kitten at the same time Brianna posted her picture of her puppy. 6 hours later he checked his phone and he had 228 likes. How many likes did he get for his adorable kitten? Who has more likes per hour? Are the rates the same? Explain. Example 3: The price of three different bags of cat food are shown in the table to the right. Which bag has the lowest price per pound? Write a verbal model of what you are comparing. For the 3.5 lb bag, price $4.83 3.5 $9.45 7 77 For the 20 lb bag, 3.5 4.83 7 9.45 20 27.20 pound 3.5 3.5 For the 7 lb bag, Cat Food Prices Size of bag Price (lbs) ($) 1 lb $27.20 20 20 20 $1.38 $1.35 1 lb $1.36 1 lb The 7 pound bag is the least expensive at $1.35 per pound Example 4: After 3.5 hours, Peyton had traveled 161miles. If she travels at a constant speed, how far will she have traveled in 4 hours? Write a verbal model of what you are comparing. Find the unit rate in miles per hour. miles hours 161 miles 3.5 3.5 hours 3.5 Multiply the unit rate, or average speed, by the number of hours traveled. 46 miles 1 hour 46 miles ( 4 hours) 184 miles 1 hour Peyton travels 184 miles in 4 hours. Complex fraction • Complex fractions are fractions that have fractions within them. They are either in the numerator, denominator, or both. • Divide complex fractions by multiplying Example 5: Jerry can jog 1⅓ miles in ¼ hour. Find his average speed in miles per hour. Write a verbal model of what you are comparing. Substitute in the values given for each quantity. miles hour 1 1 3 1 miles hour 4 Since average speed in miles per 1 hour, divide the numerator and denominator by ¼ . 44 1 miles 1 5 miles 3 4 3 1 3 1 1 1 hour 1 hour 4 4 1 1 Jerry jogs at an average speed of 5 ⅓ miles per hour. Example 6: Mr. Isaacs is spreading mulch in his yard. He spreads 4⅔ square yards in 2 hours. How many square yards can he mulch in 1 hour? Write a verbal model of what you are comparing. sq. yds. Substitute in the values given for each quantity. 2 Divide the numerator and denominator by 2 to find the unit rate. hours 4 miles 3 2 hours 14 1 1 sq. yds. 4 2 sq.yds. 3 1 3 2 3 22 1 hour 1 hour 2 2 Mr. Isaacs can mulch 2 ⅓ square yards per hour.